We develop the thermodynamic formalism for skew-periodic Z-extensions of expanding interval maps. Our formalism allows us to perform a dimensional analysis of the recurrent dynamics, as well as the transient dynamics with prescribed escape rate. We obtain explicit formulae for dimension gaps caused by transience. We also discuss the relation to Z-extensions of Kleinian groups. This is a joint work with Maik Groeger (Univ. Vienna) and Marc Kesseboehmer (Univ. Bremen).